Re: how

Am 22.04.2024 um 16:15 schrieb WM:

Le 20/04/2024 à 20:47, Richard Damon a écrit :

On 4/20/24 2:31 PM, WM wrote:

 

The interval (0, ω2) is covered by {2, 4, 6, ...}.

Unsinn. Hint: {2, 4, 6, ...} c {1, 2, 3, ...} c (0, ω) c (0, ω2).

But that interval would be actually { 1, 2, 3, 4, 5, 6, ..., ω, ω+1, ω+2, ...}
>
so, the interval notation is just incorrect as it includes members that aren't in the actual resutls.
>
So yes, the results are _in_ the interval, but are NOT THE interval.

 The results cannot be compressed to the interval (0, ω) of the set { 1, 2, 3, ...}. This shows that new numbers are generated by multiplication.

Schau Mückenhirn:
Es gilt (a) {1, 2, 3, ...} c (0, ω)
und (b) {2, 4, 6, ...} c {1, 2, 3, ...}
und damit (c) {2, 4, 6, ...} c (0, ω) .